This research work emphasizes on the development of a unique high-gain BOCUK DC-DC converter for Switched Mode Power Supply (SMPS) applications. The high-gain BOOST-CUK (BOCUK) DC-DC converter combines the benefits of both Boost and Cuk converters for attaining instantaneous line current shaping and load regulation. The proposed BOCUK converter provides a non-inverted output and improves the voltage gain and efficiency. The modes of operation of the high-gain BOCUK DC-DC Converter in a Continuous Conduction Mode (CCM) with parasitic elements in the circuit are examined and a state-space model is constructed. The second-order model is derived using the Modified Hankel Matrix Method (HMM) to make the controller design easier. Dual-loop Control employing an inner Linear Quadratic Regulator (LQR) current Controller and an outer Atom Search Optimization (ASO)-tuned Proportional Integral (PI) controller is used to analyze the performance indices of the high-gain converter and fluctuations in line, load and setpoint are investigated. Simulation results prove that the LQR controller is robust in tracking the load voltage and provides excellent line current shaping with low % Total Harmonic Distortion (THD) and nearly Unity Power Factor (UPF). The hardware model for 200W is built and implemented using the TMS320F28027F microcontroller to verify the simulation results.